Barrons AP Calculus - David Bock

FIGURE N3–4

E2. Graphically.

If we have the graph of a function f (x), we can use it to graph f ′(x). We accomplish this by estimating
the slope of the graph of f (x) at enough points to assure a smooth curve for f ′(x). In Figure N3–5 we
see the graph of y = f (x). Below it is a table of the approximate slopes estimated from the graph.

FIGURE N3–5
x −3 −2.5 −2 −1.5 −1 0 0.5 1 1.5 2 2.5
f ′(x) −6 −3 −0.5 1 2 2 1.5 0.5 −2 −4 −7
Figure N3–6 was obtained by plotting the points from the table of slopes above and drawing a
smooth curve through these points. The result is the graph of y = f ′(x).